It is an applied mathematics question The temperature Tx t o

It is an applied mathematics question.

The temperature T(x, t) of a uniform rod 0 lessthanorequalto x lessthanorequalto L satisfies the diffusion equation partial differential^2 T/partial differential x^2 = k partial differential T/partial differential t, and is initially at a uniform temperature T(x, 0) = T_0. At time t = 0 the end x = L of the rod is plunged into a bucket of ice which reduces its temperature to T = 0 but the other end of the rod has its temperature maintained at T = T_0 for all t greaterthanorequalto 0. Show how scaled variables x and t can be defined with T(x, t)/T_0 = (1 - x/L) + W (x, t) so that the governing equations and initial/boundary conditions for W are independent of all the parameters in the problem.

Solution

ANS

Try to integrate the qestion with boundary condition.